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Comment

Can nucleosomal DNA be described by an elastic model?Comment on “Sequence-dependent collective properties of DNAs

and their role in biological systems”by Pasquale De Santis and Anita Scipioni

Victor B. Zhurkin a,∗, Wilma K. Olson b,∗

a National Cancer Institute, National Institutes of Health, Bethesda, MD 20892, USAb Rutgers, The State University of New Jersey, Wright–Rieman Laboratories, 610 Taylor Road, Piscataway, NJ 08854-8087, USA

Received 27 January 2013; accepted 28 January 2013

Available online 29 January 2013

Communicated by E. Di Mauro

The review of DNA sequence-dependent conformational mechanics by Pasquale De Santis and Anita Scipioni [1] isvery timely in this year marking the 60th anniversary of the discovery of the DNA double helix. The authors providean impressive compilation of the effects of DNA sequence-dependent structure and deformability on biologicallyimportant systems, ranging from the natural curvature of DNA in solution to the positioning of nucleosomes oneukaryotic genomes.

We wish to comment on two issues – one very general, and the other rather specific.

1. Our first aim is to draw the reader’s attention to the limitations of the ‘first-order elasticity’ model which isextremely popular among researchers applying principles of theoretical mechanics to questions in DNA structuralbiology. In our opinion, this approach is appropriate for a limited number of biological problems, where DNA defor-mations are relatively insignificant; the behavior of DNA packaged in chromatin is beyond the limits of the approach.That is, the small deformations of an elastic model make sense for a theoretical description of DNA curvature, wherethe global physical properties of the system (such as the radius of gyration, end-to-end distance, etc.) are reasonablyapproximated by room-temperature (kT /2) fluctuations in the canonical double-helical structure [2,3]. Subtle varia-tions in the intrinsic spatial arrangements of specific nucleotides or characteristic differences in the local deformabilityof successive base pairs account well for the observed behavior of such systems. Another successful application of afirst-order elastic treatment of DNA is the theoretical evaluation of the global configurations and looping propensitiesof the ∼100 bp-long pieces of DNA incorporated in the GalR [4] and LacI repressosomes [5]. In these cases thesequence-dependent patterns in base-pair geometry lead to the smooth bending (and concomitant untwisting) neededto close the loops between the protein headpieces. In other words, a first-order elastic approach is suitable for systemswhere DNA is either free or ‘relatively free’ from bound proteins.

DOI of original article: http://dx.doi.org/10.1016/j.plrev.2013.01.004.* Corresponding authors.

E-mail addresses: zhurkin@nih.gov (V.B. Zhurkin), wilma.olson@rutgers.edu (W.K. Olson).

1571-0645/$ – see front matter Published by Elsevier B.V.http://dx.doi.org/10.1016/j.plrev.2013.01.009

V.B. Zhurkin, W.K. Olson / Physics of Life Reviews 10 (2013) 70–72 71

By contrast, modeling the strong distortions of DNA in chromatin with a ‘first-order elasticity approach’ is ques-tionable, to say at the least. Our assessment [6] of the best-resolved crystal structure of the nucleosome core particle[7] suggests that the highly deformed ‘kink-and-slide’ dimeric steps of DNA found near the points of contact withthe histone proteins are of the order of 10 kT higher in energy than the canonical B DNA structure. We find thesedifferences using both a ‘knowledge-based’ elastic model [8,9] and all-atom energy calculations [10]. Indeed, the con-formational features of the high-energy state are consistent with a change of DNA helical state, a BI → BII transition,which should not necessarily obey classical rod mechanics or the sequence-dependent rules of DNA deformabilityfound in intact double-helical structures. Different large-scale transitions, e.g., ‘partial melting’ at TA base-pair steps[11–13], appear to accompany the formation of other nucleosome structures (the complex of the so-called 601 DNAsequence [14] with recombinant Xenopus laevis histones). An elastic model cannot capture the strong DNA distortionsfound in nucleosomes. Prediction of nucleosome positioning requires knowledge of the multi-dimensional potentialenergy surfaces describing the likely transition pathways between the nucleosome-bound and free DNA states, as wellas understanding of the contributions of the histones to the changes in DNA helical structure.

2. Our second comment is related to the comparison made by Drs. De Santis and Scipioni between the Olson etal. [8] and Morozov et al. [15] ‘knowledge-based’ elastic models of DNA. We disagree with the authors’ claim that“the two sets of data are poorly correlated, probably, due to the more extensive database adopted by Morozov et al.[23].” In fact, the average Roll values in the two sets [8,15] rather strongly correlate, with a correlation coefficientR = 0.80. The Twist–Twist correlation is even stronger, R = 0.93. (We used the same approach as in Fig. 2 [1], thatis, asymmetric steps like AA:TT are counted twice, and symmetric steps like AT are counted once.) The number ofstructures used to evaluate the equilibrium values of the DNA parameters and rigidity matrix, however, is not criticalin this case. In particular, Balasubramanian et al. [9] generated updated elastic functions based on 135 non-redundantprotein–DNA structures (of 2.5 Å or better resolution), more than those incorporated in the two mentioned studies[8,15]. The Roll–Roll correlation between the latter dataset and that of Morozov et al. [15], R = 0.76, nevertheless,remains nearly the same as described above.

More likely, the differences between the two potentials stem from the ‘filtering’ used in our work and in thesubsequent work of Balasubramanian et al. [8,9], to exclude dimeric steps which are too close to the ends of DNAfragments or which are distorted such that the rigid-body parameters relating successive base pairs deviate from theiraverage values by more than three standard deviations. There is no mention of such filtering by Morozov et al. [15].Our assumption about the impact of DNA filtering is consistent with the fact that the average Roll angles reported byMorozov et al. span a wider range of values, from −1.4◦ (for AT) to 6.0◦ (for CA:TG), than our Roll values, whichvary from 0.3◦ (for GC) to 5.4◦ (for CG).

Finally, it is not entirely correct to compare ‘knowledge-based’ elastic models of DNA derived from protein–DNA complexes [8,9,15] with the in silico Roll values reported by De Santis and Scipioni [1]. The latter modeldoes not capture the effects of protein forces that are averaged out in statistical analyses of crystal data [8,9,15].Instead, it may be more appropriate to compare the simple in silico model of DNA elasticity [1] with recent sequence-dependent elastic models deduced from all-atom molecular dynamics simulations [16]. The latter computations hintof correlations between bases sequentially distant along DNA that may prove important in the treatment of longpolymers [17].

References

[1] De Santis P, Scipioni A. Sequence-dependent collective properties of DNAs and their role in biological systems. Phys Life Rev 2013;10:41–67[in this issue].

[2] Olson WK, Marky NL, Jernigan RL, Zhurkin VB. Influence of fluctuations on DNA curvature. A comparison of flexible and static wedgemodels of intrinsically bent DNA. J Mol Biol 1993;232:530–54.

[3] Olson WK, Zhurkin VB. Modeling DNA deformations. Curr Opin Struct Biol 2000;10:286–97.[4] Geanacopoulos M, Vasmatzis G, Zhurkin VB, Adhya S. Gal repressosome contains an antiparallel DNA loop. Nat Struct Biol 2001;8:423–36.[5] Swigon D, Coleman BD, Olson WK. Modeling the Lac repressor–operator assembly. I. The influence of DNA looping on Lac repressor

conformation. Proc Natl Acad Sci USA 2006;103:9879–84.[6] Tolstorukov MY, Colasanti AV, McCandlish DM, Olson WK, Zhurkin VB. A novel roll-and-slide mechanism of DNA folding in chromatin:

implications for nucleosome positioning. J Mol Biol 2007;371:725–38.[7] Davey CA, Sargent DF, Luger K, Mäder AW, Richmond TJ. Solvent mediated interactions in the structure of the nucleosome core particle at

1.9 Å resolution. J Mol Biol 2002;319:1097–113.

72 V.B. Zhurkin, W.K. Olson / Physics of Life Reviews 10 (2013) 70–72

[8] Olson WK, Gorin AA, Lu XJ, Hock M, Zhurkin VB. DNA sequence-dependent deformability deduced from protein–DNA crystal complexes.Proc Natl Acad Sci USA 1998;95:11163–8.

[9] Balasubramanian S, Xu F, Olson WK. DNA sequence-directed organization of chromatin: structure-based analysis of nucleosome-bindingsequences. Biophys J 2009;96:2245–60.

[10] Wang D, Ulyanov NB, Zhurkin VB. Sequence-dependent kink-and-slide deformations of nucleosomal DNA facilitated by histone argininesbound in the minor groove. J Biomol Struct Dyn 2010;27:843–59.

[11] Tan S, Davey CA. Nucleosome structural studies. Curr Opin Struct Biol 2011;21:128–36.[12] Olson WK, Zhurkin VB. Working the kinks out of nucleosomal DNA. Curr Opin Struct Biol 2011;21:348–57.[13] Chua EYD, Vasudevan D, Davey GE, Wu B, Davey CA. The mechanics behind DNA sequence-dependent properties of the nucleosome.

Nucleic Acids Res 2012;40:6338–52.[14] Thastrom A, Bingham LM, Widom J. Nucleosomal locations of dominant DNA sequence motifs for histone–DNA interactions and nucleo-

some positioning. J Mol Biol 2004;338:695–709.[15] Morozov AV, Fortney K, Gaykalova DA, Studitsky VM, Widom J, Siggia ED. Using DNA mechanics to predict in vitro nucleosome positions

and formation energies. Nucleic Acids Res 2009;37:4707–22.[16] Lankas F, Sponer J, Langowski J, Cheatham TE 3rd. DNA basepair step deformability inferred from molecular dynamics simulations. Biophys

J 2003;85:2872–83.[17] Lankas F, Gonzalez O, Heffler LM, Stoll G, Moakher M, Maddocks JH. On the parameterization of rigid base and basepair models of DNA

from molecular dynamics simulations. Phys Chem Chem Phys 2009;11:10565–88.